Supplementary Information (To Be Available Online)
Supplementary Information (to be available online)
RHESSI and Wind particle detector data analysis.
During the intense initial spike, all X- and gamma-ray detectors experienced some degree of saturation, making reliable reconstruction of the time history and energy spectrum difficult or impossible. Many small, thin silicon particle detectors, on the other hand, had very low cross-sections for X- and gamma-ray interactions, and therefore did not saturate, even though they did respond strongly to the peak. We have therefore analyzed the observations of the Wind 3D Plasma &Energetic Particle experiments14 and of the RHESSI particle monitor detector 15 with the GEANT3 and GEANT4 simulation codes to get information on the initial spike (specifically, the first kT in figure 1b, and the spectrum, time history, and kT in figure 2). The RHESSI particle detector has 25 mm2 area and is 960 microns thick. Wind has six double-ended Solid State Telescopes (SSTs), five with two back-to-back 1.5cm2, 300 micron thick silicon detectors (called O and F, with 9 and 7 PHA channels, respectively), and one SST with a third, 15 cm2 500 micron thick detector (T) in between. The multi-channel analyzers covered the 20 keV – 11 MeV range with various time resolutions between 12 and 96 s, while the RHESSI detector had two discriminators with 50 and 620 keV thresholds which were read out with 0.125 s resolution. In each case, the simulations included the matter surrounding the detectors, and attempted to reproduce the observed count rates with incoming power law, thermal bremsstrahlung, and blackbody energy spectra. In all cases, the power law and bremsstrahlung spectra were strongly rejected by the Wind data (2= 42 and 69 for 10 degrees of freedom), and only the blackbody provided an acceptable fit (2= 10 for 10 degrees of freedom). These fits were performed for the Wind detectors with the highest statistics (F and O), because they gave the strongest restriction on the error bars for the blackbody temperature (175 25 keV). A systematic error of 10% was assumed for the Wind simulations. This is a typical conservative estimate for simulations of this type; it includes uncertainties in the masses and compositions in the structure surrounding the detector, as well as uncertainties in the detector size, volume, and calibration. Fits including all the Wind detectors are also consistent with these results. An additional systematic uncertainty of 15% was included for the RHESSI data, to include the effects of absorption in the spacecraft structure and interception of photons scattered off the Earth’s atmosphere. Both these effects were modeled in GEANT3, with the prediction that 25% of the incoming photons are removed by the former process, and an approximately equal number are added by the latter process, but at lower energies, tending to soften the overall spectrum. The observed RHESSI response is consistent with the blackbody fit.
For the peak, the sum of the count rates from the 12 Wind detectors reached 1900 c/s/detector. The Wind particle detectors have a 600 ns shaping time, which is fast enough that pulse pile-up in the detectors is negligible. However, the overall throughput of the system is determined by the sampling rate of the multiplexed analog-to-digital converters, which is not well quantified at these data rates. Therefore the overall livetime of the detectors is uncertain, and the responses cannot be used to measure the fluence, even though they are well within the count rate range of measuring the spectral shape correctly. Thus Wind was used to measure the spectral shape during the spike, while the RHESSI particle detector was used to derive the normalization.
The RHESSI particle detector counted 3008 counts in the peak 125 ms of the flare. Its saturation level is approximately 105 counts in 125 ms. Thus pulse pile-up is negligible. Because this detector has only two channels, it cannot strongly constrain the spectral shape, although it can confirm or reject the spectral shapes found by the Wind detectors, and it can determine the normalization of the Wind spectra accurately. These data were used to produce the time history and kT in the inset to figure 2.
RHESSI gamma-ray detector data analysis
The RHESSI gamma-ray detectors are segmented Ge detectors which record the time and energy of each photon interaction >3 keV. They were unsaturated after the initial spike. However, there are two structures which can attenuate the incoming photons in the observations of the oscillatory phase described here. The first is a shutter which was automatically put into place over the front segments as a response to the high count rates, and remained there for the first 272 s in figure 1. The second is the imaging grid structure above the detectors, which affects both the front and rear segments for photons < 20 keV. However, as the spacecraft rotates, a direct (unattenuated) path exists to some of the detectors for brief intervals twice per rotation period. We call these intervals “snapshots”. To eliminate the effects of attenuation in Figure 1a, Figure 1a (inset), and Figure 5a (black curve), we have used counts > 20 keV. To eliminate these effects in Figure 4 and Figure 5a, we have used the snapshot data. We have also used these snapshots to obtain the spectral temperatures in figure 1b. We have used the on-axis (0) RHESSI response matrices for this analysis, which should reproduce reasonable flux numbers and spectral distributions. With the current matrices we are unable to strongly distinguish between thermal bremsstrahlung and black-body spectral fits for the tail, so we have included both in this paper. We anticipate further spectral analysis including response matrices for this source location (under construction) should discriminate between these models.
Detectability of Magnetar Flares by BATSE and Swift.
We estimated the BATSE sampling depth for MFs using our peak incident flux from this flare in the standard BATSE 50-300 keV energy range (determined from our best-fit RHESSI PD fluence and WIND spectral fit), over the BATSE trigger timescales of 64-ms, 256-ms, and 1024-ms. We find the optimal BATSE trigger timescale to be the 256-ms (BATSE's P256). Given the 50%-efficiency trigger flux for P25633 of 0.50 ph cm-1 s-1, we determine that this flare would have been detected by BATSE to a distance of 31 Mpc. As a check, we analyzed the 50-300 keV fluence of all the BATSE short-hard GRBs with durations T90 = 0.1-0.2 s, and found a threshold fluence of ~510-8 erg cm-2, corresponding to comparable detection distance. This is lower than the distance originally quoted in GCN 293638 as a result of our spectral fits - the black-body fit is much harder than typical GRB spectra, resulting in lower photon fluxes in the 50-300 keV range than a typical short-hard GRB spectrum with comparable energy flux. To estimate the Swift BAT sensitivity, we used a P256 (50-300 keV) photon flux sensitivity 5 times better than BATSE (Ref. 46, Fig. 9), corresponding to ~0.10 ph cm-2 s-1, for a limiting detection distance for BAT of 70 Mpc. As a check, the advertised energy flux sensitivity of ~10-8 erg cm-2 s-1 yields an even larger limiting distance.
To estimate the BATSE sensitivity to pulsating tails, we examined the strongest short-hard GRB seen by BATSE, trigger #6293. This GRB had a duration T90 = 0.192 s, and a total fluence of 4.3010-5 erg cm-2, dominated by photons >300 keV. Given the background count rate in the 400-s period after this burst, we estimate a 5 upper limit on a 20-100 keV tail fluence of 210-7 erg cm-2, setting the BATSE upper limit on the ratio of tail-to-peak fluence of 0.5%.
To estimate the Swift XRT sensitivity to the pulsating tails, we used the XRT response available in the HEASARC WebPIMMS package. We developed a model of the pulsating X-ray tail from our time-dependent thermal bremsstrahlung fits over the course of the 380-s tail, assuming the average 3-10 keV pulse shape. Folding the time-dependent model through the XRT response, and assuming an optimistic 20-s slew time, we estimate a marginal 0.3-10 keV detection of the soft tail at 10 - 40 Mpc for blackbody and bremsstrahlung spectra. As a check, the December 27 tail produced an incident 0.3-10 keV fluence of 0.18 - 1.610-3 erg cm-2. The quoted threshold flux for XRT detection is 210-14 erg cm-2 s-1 for a 104 s observation, corresponding to a fluence threshold of 210-10 erg cm-2. Comparing this with our measured X-ray fluence yields a comparable detection distance. We also determined that the magnetar rotation period can be picked out of the XRT data by FFTs out to distances of ~2 - 8.5 Mpc (it is clearly seen by eye out to ~1 - 4 Mpc).
Rate of magnetar flares
To estimate the rate of extragalactic magnetar flares, we needed to estimate the blue luminosity of the Milky Way, . The synthetic Galactic model of ref. 48, based upon Hipparcos data and recent large-scale surveys in the optical and infrared, implies a Galactic stellar thin disk mass . We divided this by which was found from the average of 30 MW-like galaxies of types Sb-Sc with luminosities within the Nearby Field Galaxy Survey (Sheila Kannappan, private communication).